Incrementally Passive Primal-Dual Dynamics for Real-Time Optimization

In this paper, we present a class of globally convergent primal-dual dynamics for the solution of constrained optimization commonly encountered in real-time optimal control applications. By exploiting the incremental passivity properties of the primal and the dual dynamics, and the associated input-nonlinearity, we construct a suitable antiwindup compensator that enforces a specified level of performance that captures allowable constraint violation. The ensuring dynamics can be considered a generalization of the classical Arrow- Uzawa gradient system and can easily be implemented in embedded optimal control applications.